Drafting has changed dramatically with the new collective bargaining agreement. There are really great reasons to pick under slot players early in the draft.
First, a bit on how the draft slotting system works. Each draft position in the first ten rounds has a dollar value assigned. The first pick in the draft is worth a certain dollar amount, the last pick in the tenth round is worth significantly less money.
The dollar values for the picks a team controls are summed together to form a teams "bonus pool". They can use this money to sign all of the players they draft. If you exceed this pool you must pay penalties. The first 10% is just monetary penalties, if you spend more than 10% you start forfeiting future draft picks (which also means less bonus pool money in the following years). There is a great primer here on draft slots and the penalties.
Any player a team drafts after the tenth round may be signed for up to $100k without counting against their bonus...